Nuprl Lemma : strict-majority_functionality
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[L1,L2:T List].
(strict-majority(eq;L1) = strict-majority(eq;L2) ∈ (T?)) supposing
((||L1|| = ||L2|| ∈ ℤ) and
(∀x:T. (||filter(λy.(eq y x);L1)|| = ||filter(λy.(eq y x);L2)|| ∈ ℤ)))
Proof
Definitions occuring in Statement :
strict-majority: strict-majority(eq;L),
length: ||as||,
filter: filter(P;l),
list: T List,
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
unit: Unit,
apply: f a,
lambda: λx.A[x],
union: left + right,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
deq: EqDecider(T),
so_apply: x[s],
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q
Lemmas referenced :
equal_wf,
length_wf,
all_wf,
filter_wf5,
l_member_wf,
strict-majority-property,
strict-majority_wf,
unit_wf2,
less_than_wf,
squash_wf,
true_wf,
iff_weakening_equal,
equal-unit
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
cumulativity,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
lambdaFormation,
setElimination,
rename,
applyEquality,
setEquality,
unionEquality,
unionElimination,
dependent_functionElimination,
independent_functionElimination,
productElimination,
independent_pairFormation,
independent_isectElimination,
imageElimination,
multiplyEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
inrEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[L1,L2:T List].
(strict-majority(eq;L1) = strict-majority(eq;L2)) supposing
((||L1|| = ||L2||) and
(\mforall{}x:T. (||filter(\mlambda{}y.(eq y x);L1)|| = ||filter(\mlambda{}y.(eq y x);L2)||)))
Date html generated:
2017_04_17-AM-09_09_36
Last ObjectModification:
2017_02_27-PM-05_17_32
Theory : decidable!equality
Home
Index